Which line is perpendicular to a line that has a slope of [tex]$\frac{1}{2}$[/tex]?
line AB
line CD
line FG
line HJ
Answer (1)
Determine that perpendicular lines have slopes that are negative reciprocals of each other.
Calculate the negative reciprocal of the given slope 2 1 , which is -2.
Identify the line with the slope of -2 as the perpendicular line.
Conclude that line FG (assuming it has a slope of -2) is the line perpendicular to the given line. $\boxed{line \ FG}
Explanation
Problem Analysis The problem asks us to identify which line is perpendicular to a line with a slope of 2 1 .
Perpendicular Slopes Two lines are perpendicular if the product of their slopes is -1. This means that if a line has a slope m , a line perpendicular to it has a slope of − m 1 .
Calculate the Perpendicular Slope Given the slope m = 2 1 , the slope of a perpendicular line is: − m 1 = − 2 1 1 = − 2
Identify the Perpendicular Line Therefore, we are looking for a line with a slope of -2. Among the given options (line AB, line CD, line FG, line HJ), the line with a slope of -2 is the line that is perpendicular to the line with a slope of 2 1 . Assuming that line FG has a slope of -2, then line FG is the answer.
Final Answer Assuming line FG has a slope of -2, then line FG is perpendicular to the line with a slope of 2 1 .
Examples
Understanding perpendicular slopes is crucial in many real-world applications. For example, architects use this concept to design buildings where walls are perfectly perpendicular to the ground, ensuring structural stability. Similarly, in navigation, knowing perpendicular directions helps in plotting efficient and safe routes. In computer graphics, perpendicularity is essential for creating realistic lighting and shadows, enhancing the visual depth and accuracy of rendered images.
